Data communication system, data decoding apparatus and method therefor

ABSTRACT

A reception program maps, by PC mapping, the values of message data to symbol x, which describes the combinations of M p  carrier waves of M c  carrier waves with value- 1  bits corresponding to the carrier waves to be transmitted, and receives the transmit signal created by performing transformation processing thereon to sample y. A matrix computing portion performs transformation processing on sample y′ in a parallel form including an unnecessary signal component to symbol z′. A first decoding portion sequentially performs maximum likelihood value decoding on groups of M bits of symbol z′ and finally decodes all of the symbol z′ to symbol x″. If the symbol x″ includes M p  value- 1  bits, a second decoding portion handles the symbol x″ as the final decoding result and if not, the second decoding portion performs maximum likelihood decoding on the entire symbol z′ to obtain the final decoding result.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to Japanese Patent Application No.2008-309569, filed Dec. 4, 2008, the entire disclosure of which isincorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates to a data communication system, data decodingapparatus and method therefor, which transmit transmission objectivedata in association with a symbol indicating a subset of plural carrierwaves in groups of a predetermined number of bits.

2. Description of the Related Art

For example, Y. Hou and M. Hamamura, “A novel modulation with Parallelcombinatory and high compaction multi-carrier modulation”, IEICE Trans.Fundamentals, vol. 90, no. 11, pp. 2556-2567, November 2007 (which willbe called Non-Patent Document 1) discloses a PC/HC-MCM (high compactionmulti-carrier modulation) applying PC to high definition multi-carriermodulation (HC-MCM).

However, Non-Patent Document 1 does not disclose a method that decodes,by two-level decoding, a transmit signal acquired by multi-carriermodulation.

In other words, Non-Patent Document 1 does not disclose theconfiguration including performing first decoding including maximumlikelihood decoding for decoding in small groups at a time sequentiallyplural times on the data included in a sample acquired from a transmitsignal, finally decoding all data, performing second decoding includingmaximum likelihood decoding on all or partial data patterns imaginablefrom the result of the first decoding and decoding the data only if itis decided that the result of the first decoding contains an error.

SUMMARY OF THE INVENTION

The present invention was made against the background and provides acommunication system, data decoding apparatus and method therefor withthe improvement that decodes data from a transmit signal faster and at alower error rate.

According to an aspect of the invention, there is provided acommunication system comprising: a transmitting apparatus; and areceiving apparatus, the transmitting apparatus having: a mapper formapping transmission objective data of a predetermined bit count to betransmitted to a first symbol including a first number of datadescribing combinations of a second number of carrier waves (firstnumber>second number) corresponding to all of the possible transmissionobjective data within the first number of carrier waves usable for thetransmission; a first transformer for performing a first transformationto transform the first symbol into transmission signal that includingfirst sample having third number of data by having the first symbol be afirst number×1 first vector to multiple the first vector by a firstnumber×third number (third number>first number) matrix, in which theresult of first multiplication of the first matrix by the firstnumber×the first number diagonal matrix that corresponding to themultiplication of each of a third number of data included in the firstsample obtained by the first transformation by each of secondcoefficients for third number of data included in the first sample beingequal to the result of second multiplication of an a third number×firstnumber upper triangular matrix by a third number×third numbernon-singular matrix in a complex form, and the non-singular matrix, andthe upper triangular matrix being given such that the result of thefirst multiplication and the result of the second multiplication beingequal in accordance with the first matrix and the diagonal matrix;multiplier for multiplying each of the first samples included in thetransmission signal by each of the second coefficients; and

a transmitter for transmitting the transmission signal including thethird number of signals to the receiving apparatus, the receivingapparatus having: a receiver for receiving the transmission signalhaving possibility to include a different signal component from thetransmission signal from the transmitting apparatus; a secondtransformer for performing a second transformation to transform thecomplex conjugate inverse matrix in the non-singular matrix into thesecond sample corresponding to the multiplication result of the uppertriangular matrix by the first vector by having the third number of dataincluded in the first sample included in the received transmissionsignal be a second vector of the third number×1 format to multiply thecomplex conjugate inverse matrix in the non-singular matrix by thesecond vector; a first decoder for sequentially performing firstdecoding on the data included in the third number of second sampleacquired by the second transformation and acquiring groups eachincluding the fourth number of data (the first number within the firstsymbol>fourth number to sequentially decode parts of the second symbolcorresponding to the first symbol for acquiring the entire secondsymbol; a second decoder, if there is a possibility that the secondsymbol decoded by the first decoding is identical to the first symbolcorresponding to the second symbol, for having the second symbolacquired by the first decoding be the first symbol, or if not, forperforming second decoding on all of the third number of second sampleto have the symbol acquired by the second decoding be the second symbol;and a demapper that decodes the transmission objective data from thefirst symbol acquired by the second decoder, wherein: the first decodingis implemented by performing maximum likelihood decoding on the thirdnumber of second sample with all of the results of the multiplication ofthe fourth number (the first number>fourth number) of elements withinthe first symbol by the fourth number×1 upper triangular matrix of thevector; the second decoding is implemented by selecting a combinationhaving the highest possibility of being identical to the third number ofsecond sample among the combinations of the second sample correspondingto the second symbol having no possibility of being identical to thefirst symbol, which is acquired by the first decoding; and the seconddecoding is implemented by selecting a combination having the highestpossibility of being identical to the second sample corresponding to thesecond symbol being acquired by the first decoding to have nopossibility of being identical to the first symbol among the firstsample corresponding to the second symbol including an equal number ofvalue-1 bits to that of the first symbol being acquired by replacing thenumber of value-1 bits included in the second symbol being acquired bythe first decoding to have no possibly of being identical to the firstsymbol by the number of value 0 bits within a predetermined range.

According to another aspect of the invention, there is provided a datadecoding apparatus for receiving transmission signal to decodetransmission objective data from the received transmission signalgenerated by mapping the transmission objective data including firstnumber of data each indicating a combination of a second number (firstnumber>second number) of carrier waves corresponding to all of thepossible transmission target data within the first number of carrierwaves usable for transmission to decode the transmission target datafrom the received transmit signal, the apparatus comprising: a receiverfor receiving the transmission signal having possibility to include adifferent signal component from the transmission signal; a transformerfor transforming the received transmission signal to a second samplehaving the third number of data corresponding to the first sample; afirst decoder for sequentially performing first decoding on a thirdnumber of data included in the acquired second sample to decode secondsymbol corresponding to the first symbol by sequentially decoding partsof the second symbol corresponding to the first symbol; a seconddecoder, if there is a possibility that the second symbol decoded by thefirst decoding is identical to the first symbol corresponding to thesecond symbol, for having the second symbol acquired by the firstdecoding be the first symbol, or if not, for performs second decoding onall of the data included in the second sample to have the second symbolacquired by the second decoding be the first symbol; and a demapper thatdecodes the transmission objective data from the first symbol acquiredby the second decoder.

According to another aspect of the invention, there is provided a datadecoding method for receiving transmission signal to decode transmissionobjective data from the received transmission signal generated bymapping the transmission objective data including first number of dataeach indicating a combination of a second number (first number>secondnumber) of carrier waves corresponding to all of the possibletransmission target data within the first number of carrier waves usablefor transmission to decode the transmission target data from thereceived transmit signal, the method comprising the steps of: the methodcomprising the steps of: receiving the transmission signal havingpossibility to include a different signal component from thetransmission signal; transforming the received transmission signal to asecond sample having the third number of data corresponding to the firstsample; sequentially performing first decoding on a third number of dataincluded in the acquired second sample to decode second symbolcorresponding to the first symbol by sequentially decoding parts of thesecond symbol corresponding to the first symbol; if there is apossibility that the second symbol decoded by the first decoding wouldbe identical to the first symbol corresponding to the second symbol, forhaving the second symbol acquired by the first decoding be the firstsymbol, or if not, performing second decoding on all of the data held bythe second sample to have the second symbol acquired by the seconddecoding be the first symbol; and decoding the transmission objectivedata from the first symbol acquired by the second decoding.

The communication system, data decoding apparatus and method thereforaccording to the present invention are configured to perform decodingfrom a transmit signal to data, as will be described below.

Notably, for concrete and clear description on those components, thecase where a symbol x (x₁ to x_(Mc)) and a sample y (y₁ to y_(Mt)) areused will be described as a concrete example.

The data bits included in a data stream to be transmitted are dividedinto groups of M_(pc) bits, and the data of a group of M_(pc), bits aretransmitted by one transmit signal frame.

The transmit signal uses M_(c) carrier waves for data transmission. Thevalue exhibited by each M_(pc)-bit data corresponds to any onecombination of M_(p) (where M_(p)<M_(c)) carrier waves selected fromM_(c) carrier waves and may be mapped to a first symbol x (x₁ tox_(Mc)), for example.

However, the bit count M_(pc) of data to be transmitted by one frame ofcarrier waves is limited by:

M_(pc)≦∥log_(Mc) C_(Mp)∥

(where operator ∥x∥ is an integer equal to an operand x or the highestinteger which is lower than the operand x, and _(y)C_(z) (Y>Z) is thenumber of combinations of the selections of Z items from Y items).

The first symbol x (x₁ to x_(Mc)) may be handled as, for example, anM_(c)×1 vector, be multiplied by an M_(c)×M_(t) matrix F that transformsthe first symbol to a sample y (y₁ to y_(Mt)) and thus be transformed tothe sample y (y₁ to y_(Mt)) (where it may be understood that thetransformation is processing of transforming a symbol in one domain to asample in another domain, such as a symbol in a frequency domain to asample in a time domain).

Furthermore, as necessary, the elements (y₁ to y_(Mt)) of the sample yare multiplied by the coefficients w (w₁ to w_(Mt)) of a window functionthat limits the bandwidth of a transmit signal.

The matrix F in a complex form is given as F=QR which is the valueresulting from the multiplication of a unitary matrix (orthogonal matrix(non-singular matrix) in a complex form) Q, which will be describedlater, by an M_(t)×M upper triangular matrix R in a complex form (whileit is given as WF=QR (where W=diag[w₁ to w_(Mt)]) if the sample y ismultiplied by the coefficients w of a window function when the sample yare not multiplied by the coefficients w of a window function).

The thus-acquired sample y ((y₁ to y_(Mt)) or (w₁y₁ to w_(Mt)y_(Mt)))undergoes signal processing such as serial/parallel transformation anddigital/analog transformation to a transmit signal y(t), which is thentransmitted through a transmission path on which a signal component n(t)excluding the transmit signal, such as a noise and radio interference,may possibly be superimposed on the signal y(t) is.

The communication system, data decoding apparatus and method thereforaccording to the present invention receive a transmit signal y(t)+n(t),perform processing such as analog/digital transformation andserial/parallel transformation on the received transmit signaly(t)+n(t), thus acquire the sample y′ (y′₁ to y′_(Mt)) corresponding tothe transmitted sample y (y₁ to y_(Mt)).

The sample y′ (y′₁ to y′_(Mt)) is handled as an M_(t)×1 vector Y_(Bi),and the vector y_(Bi) is multiplied by an M_(t)×M_(t)complex-conjugate-transposed (Hermit-transposed) unitary matrix (Q^(H)(which is the inverse function of the non-singular matrix)) fortransformation to a symbol z (z₁ to Z_(Mt)). (Notably, thetransformation may also be understood as processing of transforming asymbol in one domain to a sample in another domain, such as thetransformation from a sample in a time domain to a symbol in a frequencydomain).

As a result of the multiplication, the second symbol x′ (x′₁ to x′_(Mc))corresponds to the first symbol x (x₁ to x′_(Mc)).

In other words, when the second symbol x′ (x′₁ to x′_(Mc)) is handled asthe M_(c)×1 vector x_(Bi), the vector x_(Bi) and Y_(Bi) have arelationship of Y_(Bi)=FX_(Bi)=QRX_(Bi). The multiplication of thevector y_(Bi) by the complex conjugate transposed matrix Q^(H)=Q⁻¹ inthe unitary matrix Q results in Q^(H)Y_(Bi)=Q^(H)QRX_(Bi)=RX_(Bi)because F=QR as described above.

The M_(c) elements x′₁ to x′_(Mc) of the second symbol x′ (x′₁ tox′_(Mc)) are the first to M_(c)th elements in an M_(t)×1 vector Rx_(Bi),and the other elements in the vector Rx_(Bi) are 0.

Groups of M (where M<M_(c)) elements are extracted sequentially from thevector Rx_(Bi) in order from the element x′_(Mc) side. The extracted Melements sequentially undergo maximum likelihood decoding. Finally, thesecond symbol x′ (x′₁ to x′_(Mc)), which is estimated as being theclosest to the first symbol x (x₁ to x_(Mc)), is decoded (firstdecoding).

Here, when the second symbol x′ (x′₁ to x′_(Mc)) does not include equalnumbers of value-1 bits and value-0 bits to those of the first symbol x(x₁ to x_(Mc)), there is no possibilities that second symbol x′ (x′₁ tox′_(Mc)) is equal to the first symbol x (x₁ to x_(Mc)).

In this case, maximum likelihood decoding using the entire vectorRx_(Bi) that gives the second symbol x′ (x′₁ to x′_(Mc)) having thenumbers of value-1 bits and value-0 bits which have come to be equal orcloser to the first symbol by replacing 1-bit values in the secondsymbol x′ (x′₁ to x′_(Mc)) by 0-bit values and/or replacing 0-bit valuesby 1-bit values. Thus, the second symbol x′ (x′₁ to x′_(Mc)) is decoded(second decoding).

Having described that the communication system, data decoding apparatusand method therefor according to the present invention perform computingusing vector and matrices, the configurations of the vector and the rowsand columns of the matrices in the Claims, the specification anddrawings the present invention are given only for the illustrationpurpose only.

In other words, even when the vector and/or matrices in the Claims,specification and drawings of the present invention, appropriate changeof the computing thereon can allow equivalent handling between theuntransposed vector and matrices and the transposed vector and matriceswith transposition.

Having described that the configurations of the claimed vector andmatrices agree with the configurations of the vector and matrices in thespecification and drawings for avoiding complex descriptions, it shouldbe noted that the systems, apparatus and methods configured bytransposing the claimed vector and/or matrices or changing theconfiguration to a configuration which can be regarded as beingequivalent by appropriate change in computing are included in the scopeof the disclosed technology which is to be recognized by the claims ofthe present invention.

It should also be noted that the configurations in which bit values aresimply inverted or the number of bits is changed in the disclosedmatters of the present invention are included within the scope of thedisclosed technology to be recognized by the claims of the presentinvention.

The claimed technological advantages and other technological advantageswill be understood by those skilled in the art by reading detaildescriptions on embodiments illustrated in the drawings.

The attached drawings are partially included in the specification of thepresent invention and illustrate embodiments of the claimed invention.Along with the illustrations, they play a role in illustrating theprinciple of the invention.

It should be understood that the drawings referred in the specificationof the present invention may not be rendered to scale unless otherwiseindicated.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing a first transmitter that creates a transmitsignal in PC/HC-MCM by using inverse discrete Fourier transform;

FIG. 2 is a diagram showing the configuration of a receiver thatreceives a transmit signal from the transmitter shown in FIG. 1 anddecodes message data;

FIG. 3 is a configuration diagram showing a communication system inCR-PC/HC-MCM to be described as an embodiment according to the presentinvention;

FIG. 4 is a diagram illustrating a form in which an unnecessary signalcomponent is superimposed on a transmit signal on a communication lineof the communication system shown in FIG. 1;

FIG. 5 is a diagram showing a hardware configuration of thecommunication apparatus shown in FIG. 3;

FIG. 6 is a diagram showing the configuration of the transmissionprogram to be executed in the source communication apparatus shown inFIG. 3;

FIG. 7 is a table illustrating the symbol x_(B) acquired by mapping bythe PC mapping portion in the transmission program shown in FIG. 6.

FIG. 8 is a diagram showing the configuration of the reception programto be executed in the destination communication apparatus shown in FIG.3;

FIG. 9 is a diagram illustrating an M-algorithm to be used in decodingprocessing by the first decoding portion in the reception program shownin FIG. 8;

FIG. 10 is a histogram illustrating the results of acquisition of thefrequencies of appearance by a computer simulation of the bit count ofthe value 1 included in the symbol x″=[x″₁ to x″_(Mc)]^(T) in thedecoding result by the first decoding portion 322 shown in FIG. 7;

FIG. 11 is a graph showing a relationship between BER values occurringin the symbol x′ decoded by the reception program shown in FIG. 7 andthe values of E_(b)/N₀; and

FIG. 12 shows a table showing the highest amounts of computing for themaximum likelihood decoding by the communication apparatus 2 shown inFIG. 2 and decoding by the first decoding portion 322 and seconddecoding portion 324 of the reception program 32 shown in FIG. 7.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

An embodiment of the claimed invention will be described in detailbelow.

The embodiment of the claimed invention is illustrated in the attacheddrawings.

The claimed invention will be described in relation to the embodiment,but a person skilled in the art will understand that it is not intendedthat the embodiment limits the claimed invention to the discloseddetails.

Conversely, it is intended that the claimed invention includes thespirit of the claimed invention and alternatives, changes andequivalents which can be included in the claimed invention.

The claimed invention will be described concretely and in detail suchthat the claimed invention can be understood sufficiently.

However, a person skilled in the art may understand that it is notintended that the implementation of the claimed invention requires allof the matters, which will be described concretely and in detail.

Notably, known methods, procedures, components and circuits may not bedescribed in detail in order to prevent the unnecessary difficulty tounderstand the aspects of the present invention.

Unless otherwise indicated, it should be understood that the discussionsusing the terms “transmit”, “receive” and “transform” relate to anelectronic computing device in a computer system, for example, and theactions and processes by electronic devices associated therewiththroughout the entire disclosure, which will be clarified by the laterdiscussions.

The electronic computing device in a computer system, for example,operates and transforms the data expressed as a physical (andelectronic) amount within a register and memory in the computer systemto other data also expressed as a physical amount within a computersystem memory or register or other similar information storage, atransmitting device or a display device.

The present invention is also suitable for the use of other computersystems such as optical and mechanical computers.

INTRODUCTION

First of all, before describing the communication system according tothe present invention, the data transmission system relating to thecommunication system according to the present invention will bedescribed as an introduction.

Hitherto, orthogonal frequency division multiplexing (which will becalled OFDM) has been used as one of data transmission systems.

In OFDM, the ratio of the peak value to the average value of the powerof a transmit signal (which will be called peak-to-average power ratioor PAR) is large. In order to reduce the PAR, PC-OFDM applying parallelcombinatory (which will be called PC) signaling technique has beenproposed.

High-compaction multi-carrier modulation (which will be called HC-MCM)has been proposed that transmits a truncated version of signal in OFDM.However, in this system, discontinuity appears between the amplitudes oftwo consecutive signal waveforms, which causes an unnecessary increasein frequency bandwidth.

In order to overcome the malfunction, parallel combinatory HC-MCM (whichwill be called PC/HC-MCM) has been proposed in order to improve the biterror rate (which will be called BER) in HC-MCM and to reduce the PAR.

PC/HC-MCM compares a coefficient contained in a transmit signal and thecoefficients corresponding to all possible symbol.

On the basis of the comparison result, the symbol with the highestpossibility of the correspondence to the coefficient contained in thetransmit signal, that is, the symbol with the shortest distance in aEuclid space is selected. Thus, the symbol corresponding to thecoefficient contained in the transmit signal can be decoded (which maybe called maximum likelihood (or ML) decoding).

However, the maximum likelihood decoding in PC/HC-MCM requires a largeamount of computing, and the implementation requires a high computingprocessing capability and a long computing time. Therefore, for example,the efficiency implementation and an increase in performance aredifficult where M_(c)>>1 and M_(p) is approximately equal to M_(c)/2.

In order to reduce the complexity of computing in decoding processing,the present invention relates to Complexity Reduced PC/HC-MCM with animprovement by using QR decomposition (or QRD, which is decomposition ofa matrix X to an orthogonal matrix (or unitary matrix) in a complex formand an upper triangular matrix R where X=QR) algorithm and M-algorithmand adopting a decoding method with an increased efficiency.

The present invention further relates to an evaluation result describinghow CR-PC/HC-MCM can decode data with a low BER from a transmit signalon which an unnecessary signal component such as noise and radiointerference is superimposed excluding a desirable signal component.

[PC-OFDM]

Before describing CR-PC/HC-MCM, PC-OFDM on which CR-PC/HC-MCM is basedwill first be described for easier understanding.

PC-OFDM is OFDM that carries message data by PC signaling and a generalN-ary (where N is generally a symbol typified by an integer of theexponentiation of 2) amplitude and phase shift keying (N-APSK).

Taking FSK as an example, the N-ary modulation method will be furtherdescribed.

For example, in a binary (where N=2) FSK modulation method, two carrierwaves f₀ and f₁ may be used, and either data 1 or 0 may be transmittedin accordance with the transmission of either carrier wave f₀ or f₁.

Similarly, in a quaternary FSK modulation method, four carrier waves f₀to f₃ may be used, and one of data (0,0), (0,1), (1,0) and (1,1) may betransmitted in accordance with the transmission of one of the carrierwaves f₀ to f₃.

In this way, in an N-ary FSK modulation method, N carrier waves f₀ tof_(N-1) may be used, and the data for n=log₂N bits may be transmitted atone time in accordance with the transmission of one of the carrier wavesf₀ to f_(N-1).

The PC signaling technique will be further described.

The PC signaling technique combines and transmits plural carrier wavesand thus increases the bit count of data which are transmittable at onetime.

For example, two carrier waves are selected from four carrier waves andare transmitted, which means ₄C₂=6 combinations when the other twocarrier waves are not transmitted.

With the PC signaling technique, for example, M_(p) carrier waves may beselected and be transmitted from M_(c) carrier waves, and the othercarrier waves may not be transmitted. In this case, _(Mc)C_(Mp) data canbe transmitted at one time thereby (where _(x)C_(y) is a combination ofx and y (where y is to be selected from x, x and y are positive integersand x≧y), and _(x)C_(y) will also be called (x/y) for clear and simpledescriptions below).

In this way, according to the N-ary FSK modulation method, the data of 2bits (which are four data) can be transmitted at one time. On the otherhand, according to the PC signaling technique, six data can betransmitted at one time.

Furthermore, for example, according to the PC signaling technique thatselects and transmits two carrier waves from eight carrier waves,(8/2)=28 data can be transmitted at one time.

The total number of preallocated carrier waves (or carriers) will becalled M_(c), and M_(p) (M_(c)>M_(p)) will refer to the number ofcarrier waves selected for PC signaling below.

In this case, the number of message data bits M_(total) for each signalin PC-OFDM is given by Expression 1 below.

M _(total) =M _(apsk) +M _(pc)  [Expression 1]

where M_(apsk) [bit] is the number of message bits mapped to an N-aryAPSK signal point constellation (including, for example, 2 points of ±1in BPSK or 4 points of ±1±j (where j is an imaginary number unit) inQPSK) and are given by Expression 2 below.

M_(pc) [bit] is a bit count of the message data encoded to one of thecombinations (or sets) of predetermined M_(p) carrier waves within M_(c)carrier waves.

M_(apsk)=M_(p) log₂ N  [Expression 2]

In other words, the relationship among the total number M_(c) of carrierwaves to be used for transmission, M_(p) to be used for the combination,and the bit count M_(c) of the message data is given by Expression 3-1or 3-2 below.

M _(pc)≦∥log₂(M _(c) /M _(p))∥  [Expression 3-1],

which is generally

M _(pc)=∥log₂(M _(c) /M _(p))∥  [Expression 3-2]

Notably, the operator ∥x∥ used in Expression 3-1 and Expression 3-2above refers to an integer which is equal to an operand x or a highestinteger which is lower than the operator x.

PC-OFDM is modeled by Expressions 4 and 5 below.

$\begin{matrix}{{y(t)} = {\sum\limits_{n = 0}^{\infty}{s^{(n)}( {t - {nT}} )}}} & \lbrack {{Expression}\mspace{14mu} 4} \rbrack \\{{{s^{(n)}(t)} = {\sum\limits_{l = 1}^{N_{c}}{x_{l}^{(n)}^{{{j2\pi}{({l - 1})}}\Delta \; {ft}}}}},{0 \leq t < {{1/\Delta}\; f}}} & \lbrack {{Expression}\mspace{14mu} 5} \rbrack\end{matrix}$

where x_(l) ^((n)) (where l=1, 2, . . . , N) is a complex symbol to afirst carrier wave and is placed at (N+1)-ary APSK signal pointresulting from the addition of the point with an amplitude of 0 to thesignal point in a normal N-ary APSK modulation method.

In nT≦t<(n+1)T, T=1/Δf (second) is a time length of one signal inPC-OFDM, and Δf(Hz) is a frequency spacing.

Here, M_(pc) message data bits can be transmitted without N-ary APSK inPC-OFDM.

In this case, x₁ ^((n))={0,1}, and M_(total)=M_(pc).

[PC/HC-MCM]

PC-OFDM on which CR-PC/HC-MCM is based will further be described.

PC/HC-MCM is divided into two systems of modulated and unmodulatedPC/HC-MCM. Modulated PC/HC-MCM transmits a signal in a truncated signalwaveform.

On the other hand, unmodulated PC/HC-MCM transmits a signal in atruncated signal waveform without N-ary ASK modulation.

Therefore, the signal in PC/HC-MCM can be modeled as Expression 6.

$\begin{matrix}{{{s^{(n)}(t)} = {\sum\limits_{l = 1}^{N_{c}}{x_{l}^{(n)}^{{{j2\pi}{({l - 1})}}{\Delta {ft}}}}}},{0 \leq t < T}} & \lbrack {{Expression}\mspace{14mu} 6} \rbrack\end{matrix}$

where T<1/Δf.

[Transmitter 20]

The unmodulated PC/HC-MCM will be described that substantially makes themost of preferred characteristics of PC/HC-MCM below.

The unmodulated PC/HC-MCM will be simply called PC/HC-MCM below.

FIG. 1 is a diagram showing a first transmitter 20 that creates atransmit signal in (IDFT-based) PC/HC-MCM by using inverse discreteFourier transform (which will be called IDFT).

As shown in FIG. 1, the first transmitter 20 includes a timing controlportion 200, a serial/parallel transforming portion (S/P) 202, a PCmapping portion 204, an IDFT portion 206, a coefficient setting portion208, multiplexing portions 210-1 to 210-M₁, a parallel/serialtransforming portion (P/S) 212 and a digital/analog transforming portion(D/A) 214.

Notably, identical numbers are given to the components which aresubstantially identical in the drawings.

The transmitter 1 creates a signal in PC/HC-MCM through thosecomponents.

The transmitter 20 may be implemented as software that operates on asignal processing apparatus having a DSP (or Digital Signal Processor)and an analog/digital transforming device (which is also true for areceiver 22 to be described with reference to FIG. 2).

The timing control portion 200 controls the timings of the processing bythe components in the transmitter 20.

The S/P 202 transforms the message data bits of M_(pc) bits input in aserial form to the one in a parallel form and outputs the result to PCmapping portion 204.

The PC mapping portion 204 maps the message data bits of M_(pc) bitsinput from the S/P 202 with combinations of M_(c) carrier waves withinMp carrier waves, as described above regarding the PC signalingtechnique.

The PC mapping portion 204 performs mapping by handling the value of thebit corresponding to M_(p) carrier waves in association with the valueof the message data of M_(pc) bits within the bits of a symbol x (x₁ tox_(Mc)) including M_(c) bits as 1 and the value of the other output bitsas 0. The PC mapping portion 204 then handles the symbol x (x₁ tox_(Mc)) acquired as a result of the mapping as the first to M_(c)thinputs of the IDFT portion 206.

Notably, the number M_(c) of carrier waves, the number M_(p) of carrierwaves selected from M_(c) carrier waves is selected so as to satisfyExpression 3 for the message data bit count M_(pc).

The PC mapping portion 204 handles the numerical value 0 as K₀ inputsubsequent to (M_(c)+1)th input to the IDFT portion 206 as padding.

The IDFT portion 206 receives the mapped message data bits from the PCmapping portion 204, performs inverse discrete Fourier transform (IDFT)processing thereon, and transforms the message data bits in a frequencydomain to one in a time domain.

As a result of the IDFT processing, (M_(t)+K₀) samples are acquired.

The IDFT portion 206 removes (M_(c)+K₀−M_(t) (where M_(c)<M_(t)+K₀))samples among them and outputs the result to the multiplexing portion212-1 to 212-M_(t) as the sample y (y₁, y₂, . . . , Y_(Mt)) resultingfrom the inverse discrete Fourier transform.

Notably, the processing of removing (M_(c)+K₀−M_(t)) samples from thesample acquired as a result of the inverse discrete Fourier transformcorresponds to truncating a signal waveform by a rectangular windowfunction in a time domain in PC/HC-MCM.

The coefficient setting portion 208 outputs the coefficients w₁ tow_(Mt) to be multiplied by the elements of the sample y (y₁, y₂, . . .and y_(Mt)), which are defined by Expression 7 below and output from theIDFT portion 206 to the multiplexing portion 210-1 to 210-M_(t),respectively.

Notably, the coefficients w₁ to w_(Mt) are coefficients of the windowfunction for waveform shaping on a transmit signal output from thetransmitter 20.

For the waveform shaping, a wide variety of window functions may beused, but the case where a coefficient of the window function expressedby Expression 7 for the purpose of the limitation of the band is aconcrete example.

w _(i)=sin [(i−1)π/M _(t)] (where i=1 to M_(t))  [Expression 7]

The PS 212 transforms the sample y (y₁, y₂, . . . , y_(Mt)) as a resultof the inverse discrete Fourier transform, which is input in a parallelform from the multiplexing portion 210-1 to 210-M_(t), to those in aserial form and outputs them to the D/A 214.

The D/A 214 transforms the result of the inverse discrete Fouriertransform in a digital form, which is input in a serial form from the PS212, to that in an analog form and thus creates and outputs the transmitsignal y(t).

The transmit signal y(t) further undergoes processing such as frequencytransformation and power amplification and are transmitted as transmitsignal to the apparatus in the receiver side through a communicationline, such as a radio communication path, on which an unnecessary signalcomponent such as noise may possibly be superimposed.

[Receiver 22]

The receiver 22 that receives a transmit signal created by thetransmitter 20 (refer to FIG. 1) and transmitted through a radiotransmission path, for example, and uses a DFT to decode message datawill be described below.

FIG. 2 is a diagram showing the configuration of the receiver 22 thatreceives a transmit signal from the transmitter 20 shown in FIG. 1 anddecodes message data.

As shown in FIG. 2, the receiver 22 includes a timing control portion200, an analog/digital transforming portion (A/D) 220, an S/P 202, adiscrete Fourier transform (DFT) 222, a decision portion 224 and a P/S212.

The receiver 22 receives a transmit signal in PC/HC-MCM from thetransmitter 20, which is the other communication party, through thosecomponents and decodes message data.

As shown in FIG. 2, an unnecessary signal component such as additivewhite Gaussian noise (or AWGN) n(t) is superimposed, in a radiotransmission path, on transmit signal y(t) from a communicationapparatus 2 which is the other communication party.

In a reception program 34, the timing control portion 200 controls thetimings for processing by the components in the receiver 22.

The A/D 220 transforms the transmit signal y(t)+n(t) in an analog form,which is received through the radio transmission path (in FIG. 3), isacquired by signal processing such as amplification and frequencytransformation and is the result of the addition of additive whiteGaussian noise n(t), for example, to that in a digital form and outputsit to the S/P 202.

The S/P 202 transforms the transmit signal in a digital form, which isinput serially from the A/D 220 to M_(t) samples y′₁ to y′_(Mt) in aparallel from and outputs it to the DFT portion 222.

The DFT portion 222 accepts the samples y′₁ to y′_(Mt) from the S/P 100as the first to M_(t)th inputs, performs discrete Fourier transform(DFT) on the received samples in a time domain, creates M_(t) samples z′(z′₁ to z′_(Mt)) in a frequency domain and outputs them to the decisionportion 224.

The decision portion 224 decides what kind of PC (parallel combinatory)signal has been transmitted from the receiver 223.

In other words, the decision portion 224 performs the processingcorresponding to the PC mapping portion 204 in the receiver 22 (inFIG. 1) and decides the one having the highest possibility ofcorrespondence to M_(t) samples z′(z′₁ to z′_(Mt)) input from the DFT222, within a set B^((n)) of all carrier waves possibly usable forM_(pc)-bit message data, to perform maximum likelihood decoding.

The set B^((n)) of carrier waves includes all of M_(t) replica samplez_(b,k) (z_(b,1) to z_(b,Mt)), which may be possibly created inaccordance with the value of all possible M_(pc)-bit message data. Thefirst element index bit of each of the samples z (z₁ to z_(Mt)) is aninteger indicating M_(pc)-bit message data corresponding to the samplez_(b,k) (z_(b,1) to z_(b,Mt)).

In order to perform the decision, the decision portion 224 finds out aset B′ of carrier waves satisfying Expression 8 below from the set BεCof all possible carrier waves.

$\begin{matrix}{B^{\prime} = {\arg {\min\limits_{B \in C}( {{J(B)} = {\sum\limits_{k = 1}^{N_{c} + K_{0}}{{{\hat{z}}_{k} - z_{B,k}}}^{2}}} )}}} & \lbrack {{Expression}\mspace{14mu} 8} \rbrack\end{matrix}$

where “arg” refers to a declination of a complex number, and “arg min”refers to “minimize evaluation function”.

Notably, the replica sample z_(b,k) (z_(b,1) to z_(b,Mt)) is defined asthe entire replica sample z_(b,k) which may possibly acquired from thetransmit signal excluding noise.

In other words, the replica sample z_(b,k) (z_(b,1) to z_(b,Mt)) is thesample z_(b,k) (z_(b,1) to z_(b,Mt)) acquired by performing DFTprocessing by the DFT 222, directly without through a transmission path,on the entire sample y (y₁ to y_(Mt)), which is acquired by performingIDFT processing by the IDFT portion 206 on the entire symbol x (x₁ tox_(Mc)), which is acquired by mapping by the PC mapping portion 204 onall of the message data bits of M_(pc) bits.

The decision portion 224 compares, as expressed in Expression 9, thereplica sample z_(b,k) (z_(b,1) to z_(b,Mt)) and the sample z′ (z′₁ toz′_(Mt)) including noise, which is acquired by the reception, andselects the replica sample z_(b,k) having the highest possibility ofbeing identical to the sample z′ (z′₁ to z′_(Mt)) including noise.

The decision portion 224 outputs the M_(pc)-bit message datacorresponding to the symbol x′ (x′₁ to x′_(Mc)) indicated by the indexof the replica sample z_(b,k) selected as described above to the P/S 212as the demodulation result.

The P/S 212 transforms the message data input in a parallel form to onein a serial form and externally outputs the result.

[Communication System 1 Applying CR-PC/HC-MCM]

An embodiment of CR-PC/HC-MCM according to the present invention will bedescribed below.

FIG. 3 is a configuration diagram showing the communication system 1 inCR-PC/HC-MCM to be described as an embodiment according to the presentinvention.

FIG. 4 is a diagram illustrating a form in which an unnecessary signalcomponent is superimposed on a transmit signal on a communication lineof the communication system 1 shown in FIG. 1.

As shown in FIG. 3, in the communication system 1, an informationprocessing apparatus 100-1 connecting to a network, for example, and acommunication apparatus 2-1 are connected, an information processingapparatus 100-2 connecting to a network, for example, and acommunication apparatus 2-2 having a substantially similar configurationto that of the communication apparatus 2-1 are connected, and thecommunication apparatus 2-1 and 2-2 are connected through acommunication line such as a radio transmission path.

Notably, as shown in FIG. 4, on the communication line of thecommunication system 1, an unnecessary signal such as additive whiteGaussian noise (or AWGN) n(t) is superimposed on a transmit signaltransmitted from the communication apparatus 2-1.

The information processing apparatus 100-1 and 100-2, for example, willbe simply called information processing apparatus 100, for example,below if specific identification of the components is not necessary.

Notably, the information processing apparatus 100 in the communicationsystem 1 may be a computer connectable to the communication apparatus 2and a network, for example, between which message data can be receivedand be transmitted.

[Hardware Configuration]

FIG. 5 is a diagram showing a hardware configuration of thecommunication apparatus 2 shown in FIG. 3.

As shown in FIG. 5, the communication apparatus 2 includes a data inputinterface (IF) 120, a DSP 122, a DSP memory 124, a data input interface126 that receives and transmits message data from and to the informationprocessing apparatus 100, a receiving portion (Rx) 128, a transmittingportion 130 (Tx), a CPU 132, a CPU memory 134 and a user interfaceportion 136.

The source the communication apparatus 2 receives message data fromthose components, creates a transmit signal in CR-PC/HC-MCM andtransmits it to the destination communication apparatus 2 through aradio transmission path.

The destination communication apparatus 2 receives the transmit signalin CR-PC/HC-MCM from the source the communication apparatus 2 throughthe radio transmission path, combines it with message data and outputsthe result to the information processing apparatus 100.

For clear and concrete description, the case where the processing by thecommunication apparatus 2 is implemented by software will be illustratedbelow. However, the processing by the communication apparatus 2 may beimplemented by special hardware or a combination of special hardware andsoftware.

Illustrating the configuration in FIG. 3 in which the communicationapparatus 2 has the DSP 122 and the CPU 13, the communication apparatus2 may have either one of them in accordance with some specifications ofand requested performance by the communication apparatus 2.

In the communication apparatus 2, the data input interface 120 receivesmessage data from the information processing apparatus 100 and outputsit to the DSP 122.

The receiving portion 128 transforms a transmit signal at a transmissionfrequency band, which is received from the communication apparatus 2 ofthe other communication party through the antenna 102 to a transmitsignal at a baseband in an analog form and outputs the result to the DSP122.

The DSP 122 has an analog/digital transforming device and adigital/analog transforming device (not shown) and executes transmissionand reception programs (which will be described later with reference toFIG. 6 and FIG. 8) modulates the message data in a digital form, whichis input from the information processing apparatus 100 withCR-PC/HC-MCM, creates a transmit signal at the baseband, and outputs itto the transmitting portion 130.

The transmitting portion 130 transforms the transmit signal inCR-PC/HC-MCM at the baseband in a digital form, which is input from theDSP 122, to a transmit signal at a transmission frequency band, andtransmits it to the communication apparatus 2 of the other communicationparty through a communication line such as a radio transmission path.

The CPU 132 executes a program stored in the CPU memory 134 controls thecomponents of the communication apparatus 2 in accordance with anoperation by a user on the user interface portion 136.

[Transmission Program]

A transmission program 30 that creates and transmits a transmit signalin CR-PC/HC-MCM will be described below.

FIG. 6 is a diagram showing the configuration of the transmissionprogram 30 to be executed in the source communication apparatus 2 shownin FIG. 3.

As shown in FIG. 6, the transmission program 30 includes a timingcontrol portion 200, an S/P 202, a PC mapping portion 204, a matrixcomputing portion 300, a coefficient setting portion (F) 208,multiplexing portions 210-1 to 210-M_(t), a P/S 212 and a D/A 214.

In other words, the transmission program 30 includes a matrix computingportion 300 which replaces the IDFT portion 206 in the transmitter 20shown in FIG. 1. The matrix computing portion 300 has the same functionas that of the IDFT portion 206.

The transmission program 30 may be supplied to the communicationapparatus 2 over a network, for example, and through the informationprocessing apparatus 100, is loaded to the DSP memory 304 or CPU memory314, is executed by concretely using a hardware resource in thecommunication apparatus 2 on an OS (not shown) that operates in the DSP302 or CPU 312 (and the same is true for the following programs).

The transmission program 30 uses those components to modulate themessage data input from the information processing apparatus 100 withCR-PC/HC-MCM and creates transmit data at a baseband in an analog form.

Notably, the numerical values Mp, M_(c), M_(pc) and M_(t) to be used inthe transmission program 30 and reception program 34 may be adjusted andbe optimized on the basis of calculations or actual measurement inaccordance with the tradeoffs among the processing by the communicationapparatus 2, the capability, the BER characteristic and the spectrumefficiency.

FIG. 7 is a table illustrating the symbol x_(B) acquired by mapping bythe PC mapping portion 204 in the transmission program 30 shown in FIG.6.

FIG. 7 shows a concrete example in a case where the bit count of messagedata is M_(pc)=4, the total number of carrier waves is M_(c)=8, thenumber of selected carrier waves is M_(p)=2, and the bit count of thesymbol is M_(t)=8 ((where M_(c)/M_(p))=(8/2)).

The differences between the transmitter 20 and the transmission program30 will be described below.

In the transmission program 30, the PC mapping portion 204, as in thetransmitter 20, maps M_(pc)-bit message data externally input throughthe data input IF 120 and transformed to a parallel form by the S/P 202to M_(t) bit symbol x_(B)=[x₁ to x_(Mt) (in FIG. 7, x₁ to x₈)]^(T)(where T indicates transposition).

In the concrete example shown in FIG. 7, the PC mapping portion 204 maps4 (M_(pc)) bit message data (0001 to 1111) to a combination of twocarrier waves selected from 8 (M_(c)) carrier waves and creates 8(M_(c)) bit symbol x_(B)=[x₁ to x₈]^(T) including 1 of 2 (M_(r)) bitsand 0 of 6 (M_(c)−M_(p)) bits.

Notably, the PC mapping portion 204 in the transmission program 30outputs the symbol x_(B) to the matrix computing portion 300 withoutadding K₀ bits of the value 0, unlike in the transmitter 20.

The matrix computing portion 300 performs transformation (which is thefirst transformation) on the symbol x_(B)=[x₁ to x_(c)]^(T) input fromthe PC mapping portion 204 by multiplying it with the M_(c)×M_(t) matrixF, which transforms them to M_(t) complex samples y=[y₁ to y_(Mt)]^(T)expressed by Expression 10, and outputs the sample y=[y₁ to y_(Mt)]^(T)acquired as Fx_(B) as a result of the multiplication to the multiplexingportion 210-1 to 210-M_(t), respectively.

$\begin{matrix}{F = \begin{bmatrix}\omega_{1,1} & \ldots & \omega_{1,M_{c}} \\\vdots & \ddots & {\vdots,} \\\omega_{M_{t,1}} & \ldots & \omega_{M_{t},M_{c}}\end{bmatrix}} & \lbrack {{Expression}\mspace{14mu} 10} \rbrack\end{matrix}$

However, the elements of the matrix F are defined by Expression 11.

$\begin{matrix}{\omega_{m,l} = {\frac{1}{\sqrt{M_{c} + M_{0}}}^{j\frac{2\pi {({l - 1})}{({m - 1})}}{{Mc} + M_{0}}}}} & \lbrack {{Expression}\mspace{14mu} 11} \rbrack\end{matrix}$

The multiplexing portion 210-1 to 210-M_(t) multiply the elements of thesample y=[y₁ to y_(Mt)]^(T) by the coefficients w₁ to w_(Mt) (refer toExpression 7), respectively, created by the coefficient setting portion208.

The sample y=[y₁ to y_(Mt)]^(T) acquired as the multiplication result bythe multiplexing portion 210-1 to 210-M_(t) is represented as WFx_(B) byusing the M_(t)×M_(t) diagonal matrix W expressed in Expression 12.

$\begin{matrix}\begin{matrix}{W = {{diag}\lbrack {w_{1},w_{2},\ldots \mspace{14mu},w_{Mt}} \rbrack}} \\{= \begin{bmatrix}{w_{1},} & \; & 0 & \; \\\; & {w_{2},} & \; & \; \\\; & \; & \ddots & \; \\0 & \; & , & w_{Mt}\end{bmatrix}}\end{matrix} & \lbrack {{Expression}\mspace{14mu} 12} \rbrack\end{matrix}$

Notably, the matrices F and W expressed in Expression 10 and Expression11 have a relationship of WF=QR between complex conjugate transpositionmatrix Q (in Expression 13) in an M_(t)×M_(t) unitary matrix Q^(H),which is to be used for transforming the sample y′=[y′₁ to y′_(Mt)]included in the received transmit signal to symbol z′=[z′₁ to z′_(Mc)],and the M_(t)×M_(c) upper triangular matrix R (in Expression 14), whichis acquired in accordance with the value of the multiplication resultWF, in a reception program 32, which will be described later withreference to FIG. 8.

Notably, as described above, H refers to a complex conjugatetransposition of a matrix, and Q^(H)=Q⁻¹ (where Q⁻¹ is the inversematrix of Q) because the matrix Q is a unitary matrix as describedabove.

For clear description, the matrices Q and R will be described which isused when the matrix W is not considered, that is, when the coefficientsetting portion 208 and multiplexing portion 210 are omitted in thetransmission program 30.

$\begin{matrix}{Q = \begin{bmatrix}q_{1,1} & \ldots & q_{1,M_{t}} \\\vdots & \ddots & \vdots \\q_{M_{t},1} & \ldots & q_{M_{t},M_{t}}\end{bmatrix}} & \lbrack {{Expression}\mspace{14mu} 13} \rbrack \\{R = {\begin{bmatrix}a_{1,1} & a_{1,2} & \ldots & a_{1,M_{c}} \\0 & a_{2,2} & \ddots & \vdots \\\vdots & \ddots & \ddots & \vdots \\0 & 0 & \ddots & a_{M_{c},M_{c}} \\\vdots & \vdots & \ddots & \vdots \\0 & 0 & \ldots & 0\end{bmatrix}{\begin{matrix}(1) \\(2) \\\vdots \\( M_{c} ) \\\vdots \\( M_{t} )\end{matrix}.}}} & \lbrack {{Expression}\mspace{14mu} 14} \rbrack\end{matrix}$

The sample y=[y₁ to y_(Mt)] created in the manner described above aretransformed to transmit signal at the baseband y(t) by the P/S 212 andD/A 214, are further transformed to the transmit signal compliant withthe communication line by the transmitting portion 130 (in FIG. 5) andare transmitted to the destination communication apparatus 2 through theantenna 102 (in FIG. 3).

As described above, unnecessary signal component n(t) such as AWGN issuperimposed on the transmit signal, on the communication line, and theresulting transmit signal are received as transmit signaly′(t)=y(t)+n(t) by the destination communication apparatus 2.

[Reception Program]

The reception program 32 that decodes message data bits from thetransmit signal in CR-PC/HC-MCM will be described below.

FIG. 8 is a diagram showing the configuration of the reception program32 to be executed in the destination communication apparatus 2 shown inFIG. 3.

As shown in FIG. 8, the reception program 32 includes a timing controlportion 200, an S/P 202, a matrix computing portion 320, a firstdecoding portion 322, a second decoding portion 324 and a PC demappingportion 326.

In other words, the reception program 32 includes the matrix computingportion 320, first decoding portion 322, second decoding portion 324 andPC demapping portion 326, which replace the DFT 222 and the decisionportion 224 in the receiver 22 (in FIG. 2).

The transmit signal received from the source the communication apparatus2 through the communication line and antenna 102 (in FIG. 3) aretransformed to the transmit signal at the baseband y′(t)=y(t)+n(t) bythe receiving portion 128. The A/D 220 and S/P 202 outputs the transmitsignal y′(t)=y(t)+n(t) to the matrix computing portion 320 as sampley′=WFx_(B)+η=[y′₁ to y′_(Mt)] (where η is an M_(t)×1 vector indicatingan unnecessary signal component) in a parallel form.

The matrix computing portion 320 transforms the sample y′ (secondtransformation) by multiplying them by the complex conjugatetransposition matrix Q^(H) in the unitary matrix and outputs the samplez′=Q^(H)(WFx_(B)+η)=Q^(H)WFx_(B)+Q^(H)η=[z′₁ to z′_(Mc)]^(T) acquired asthe multiplication result to the first decoding portion 322.

The information matrices F and W are shared between the transmissionprogram 30 and the reception program 32. In advance, the first decodingportion 322 acquires the matrix Q (by Expression 13) and matrix R (byExpression 14) in accordance with the value of the matrix F (WF inreality by Expression 11 and Expression 12) to be used in thetransmission program 30 and further acquires the replica symbol Rx_(Bi)which is acquired by multiplying all possible symbol x_(Bi)=[x_(i1) tox_(Mc)]^(T) by the matrix R, as expressed in Expression 15.

The replica symbol Rx_(Bi) can be defined as the resultQ^(H)QRx_(Bi)=Q⁻¹QRx_(Bi)=Rx_(Bi) (WFx_(Bi) in reality) of themultiplication of the symbol x_(B)i=[x_(i1) to x_(iMc)]^(T) created bythe PC mapping portion 204 in the transmission program 30 by the matrixF and the multiplication of the multiplication result Fx_(B)i (WFx_(Bi)in reality)=QRx_(Bi) (QWFx_(Bi) in reality) by the complex conjugatetransposition matrix Q^(H)(=Q⁻¹) in the matrix Q without notsuperimposition of an unnecessary signal component thereon.

$\begin{matrix}{{Rx}_{\mathcal{B}_{i}} = {\begin{bmatrix}{{a_{1,1}x_{i,1}} + \ldots + {a_{1,M_{c}}x_{i,M_{c}}}} \\\vdots \\\vdots \\\vdots \\{{a_{{M_{c} - 1},{M_{c} - 1}}x_{i,{M_{c} - 1}}} + {a_{{M_{c} - 1},{M_{c} - 1},M_{c}}x_{i,M_{c}}}} \\{a_{M_{c},M_{c}}x_{i,M_{c}}} \\0 \\\vdots \\0\end{bmatrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}\begin{matrix}( M_{c} ) \\\vdots\end{matrix} \\(M)\end{matrix} \\\vdots\end{matrix} \\(2)\end{matrix} \\(1)\end{matrix} \\\;\end{matrix} \\\;\end{matrix} \\,\end{matrix}}} & \lbrack {{Expression}\mspace{14mu} 15} \rbrack\end{matrix}$

Notably, in Expression 15, x_(i,l) (where l=1 to M_(c)) is the lthelement in the vector x_(Bi).

[Decoding Processing by First Decoding Portion 322]

FIG. 9 is a diagram illustrating an M-algorithm to be used in decodingprocessing by the first decoding portion 322 in the reception program 32shown in FIG. 8.

Notably, FIG. 9 shows the processing where M_(c)=4, M_(p)=2 and M=2 as aconcrete example.

[Outline of Decoding Processing]

First of all, the outline of the decoding processing applyingM-algorithm by the first decoding portion 322 will be described. Thedecoding processing applying M-algorithm by the first decoding portion322 is performed through step 1 to step (M_(c)−M) below.

[Step 1] The set of vector x_(u) ⁽⁰⁾ expressed in Expression 16 ismultiplied by the matrix R and is handled as the first set Rx_(u) ⁽⁰⁾ ofreplica symbol in M-algorithm expressed in Expression 16.

The set of replica symbol Rx_(u) ⁽⁰⁾ is used to perform the maximumlikelihood decoding expressed in Expression 17, whereby bit valuesx′_(Mc) are acquired.

Furthermore, the set of vector x_(u) ⁽¹⁾ including the bit valuesx′_(Mc) acquired by the processing as the lowest element as expressed inExpression 18 is created.

[Step 2] The created set of vector x_(u) ⁽¹⁾ is multiplied by the matrixR, the second set of replica symbol Rx_(u) ⁽¹⁾ is created.

The second set of replica symbol Rx_(u) ⁽¹⁾ is used to perform themaximum likelihood decoding expressed in Expression 17, whereby bitvalues x′_(Mc)−1 is acquired.

Furthermore, the set of vector x_(u) ⁽²⁾ including the bit valuesx′_(Mc) to x′_(Mc-1) acquired by the processing as the lowest and secondelements as expressed in Expression 18 is created.

[Step (M_(c)−M−1)] The processing in steps 1 and 2 above is performedM_(c)−M−2 times, the set of vector x_(u) ^((Mc-M-2)) created by the(M_(c)−M−2)th processing is multiplied by the matrix R, whereby the(M_(c)−M−1)th set of replica symbol Rx_(u) ^((Mc-M-2)) is created.

The (M_(c)−M−1)th set of replica symbol Rx_(u) ^((Mc-M-2)) is used toperform the maximum likelihood decoding, which is similar to the firstand second ones, whereby the bit values x′_(Mc-M-2) is acquired.

Furthermore, the set of vector x_(u) ^((Mc-M-1)) including the bitvalues x′_(Mc) to x′_(Mc-M-2) acquired by the processing as the first to(M_(c)−M−1)th elements from the bottom is created.

[Step (M_(c)−M)] Up to this point, the processing in steps 1 to(M_(c)−M−1) is performed, and when M elements are included in the symbolRx_(u) ^((Mc-M-1)), the maximum likelihood decoding is performed on theentire M elements. Then, all of the bit values of the symbol aredecoded.

[Details of Decoding Processing]

The decoding processing by the first decoding portion 322 will bedescribed in further details below.

The first decoding portion 322 uses M-algorithm to perform decodingprocessing on the symbol z′=[z′₁ to z′_(Mc)]^(T) input from the matrixcomputing portion 320 as described below.

First of all, as in the 0th step in FIG. 9, all (U₀) bit arrays of the(M_(c)−M)th to M_(c)th M elements (x_(i,Mc-M) to x_(i,Mc)) of the symbolx_(Bi)=[x_(i,1) to x_(i,Mc)]^(T) are prepared, and M_(c)−M₀ are added tothe upper parts of all of them, whereby the M_(c)×1 vector x_(u) ⁽⁰⁾(where u=1, 2, . . . , U₀≦2^(M)) expressed in Expression 16 are created.

$\begin{matrix}{x_{u}^{(0)} = \lbrack {\overset{\overset{M_{c} - {M\; 0s}}{}}{0\mspace{14mu} 0\mspace{14mu} \ldots \mspace{14mu} 0}\mspace{14mu} \overset{\overset{M\mspace{14mu} {elements}}{}}{x_{u,{M_{c} - M}}\mspace{14mu} x_{u,{M_{c} - M + 1}}\mspace{14mu} \ldots \mspace{14mu} x_{u,M_{c}}}} \rbrack^{T}} & \lbrack {{Expression}\mspace{14mu} 16} \rbrack\end{matrix}$

The first decoding portion 322 further performs computing in Expression17, and the values of the M_(c)th bits of the symbol x_(Bi)=[x_(i,1) tox_(i,Mc)]^(T) are acquired.

$\begin{matrix}{x_{M_{c}}^{\prime} = {x_{u,M_{c}} = {\arg {\min\limits_{u}( {{{Q^{H}y^{\prime}} - {Rx}_{u}^{(0)}}} )}}}} & \lbrack {{Expression}\mspace{14mu} 17} \rbrack\end{matrix}$

Next, in the first step in FIG. 9, the first decoding portion 322handles the value of the bit acquired in the 0th step as the M_(c)thelement x′_(Mc), prepares all (U₁) bit arrays of the (M_(c)−M−1)th to(M_(c)−1)th M elements (xi, _(Mc-M-1) to x_(i) and _(Mc-1)) of thesymbol x_(Bi)=[x_(i,1) to X_(i,Mc)]^(T), adds M_(c)−M−1 0 s to the upperparts of all of them, creates the M_(c)×1 vector x_(u) ⁽¹⁾ (u=1, . . . ,U₁≦2^(M)) in the configuration expressed in Expression 18.

$\begin{matrix}{x_{u}^{(1)} = \lbrack {\overset{\overset{M_{c} - M - {10s}}{}}{0\mspace{14mu} 0\mspace{14mu} \ldots \mspace{14mu} 0}\mspace{14mu} \overset{\overset{M\mspace{14mu} {elements}}{}}{x_{u,{M_{c} - M - 1}}x_{u,{M_{c} - M - 2}}\mspace{14mu} \ldots \mspace{14mu} x_{u,{M_{c} - 1}}}x_{M_{c}}^{\prime}} \rbrack^{T}} & \lbrack {{Expression}\mspace{14mu} 18} \rbrack\end{matrix}$

Furthermore, the first decoding portion 322 performs the computing inExpression 19 and acquires the value of the (M_(c)−1)th bit in thesymbol x_(Bi)=[x_(i,1) to x_(i,Mc)]^(T).

$\begin{matrix}{x_{M_{c} - 1}^{\prime} = {x_{u,{M_{c} - 1}} = {\arg {\min\limits_{u}( {{{Q^{H}y^{\prime}} - {Rx}_{u}^{(1)}}} )}}}} & \lbrack {{Expression}\mspace{14mu} 19} \rbrack\end{matrix}$

Sequentially in the nth step (where n=1 to M_(c)−M), the first decodingportion 322 further handles the value of the bit acquired up to the(n−1)th step as the M_(c)th to M_(c-n-1)th elements x′_(Mc) tox′_(Mc-n-1), prepares all (U_(n)) bit arrays of the (M_(c)−M−n) th to(M_(c)−n) th M elements (x_(i), _(Mc-M-n) to x_(i) and _(Mc-n)) of thesymbol x_(Bi)=[x_(i,1) to x_(i,Mc)]^(T), adds M_(c)−M−n 0 s to the upperparts of all of them, and creates an M_(c)×1 vector x_(u) ^((n)) (u=1,2, . . . , U_(n)≦2^(M)).

The first decoding portion 322 further performs the computing inExpression 20 and acquires the value of the (1-M)th bit of the symbolx_(Bi)=[x_(Bi1) to x_(BiMc)]^(T).

Notably, in the final (n=M_(c)−M)th step, the values of the first toM_(t)h bits of the symbol x_(Bi)=[x_(i,1) to x_(i,Mc)]^(T) are acquiredby one operation.

$\begin{matrix}{x_{M_{c} - n}^{\prime} = {x_{u,{M_{c} - n}} = {\arg {\min\limits_{u}( {{{Q^{H}y^{\prime}} - {Rx}_{u}^{(n)}}} )}}}} & \lbrack {{Expression}\mspace{14mu} 20} \rbrack\end{matrix}$

As described above, the first decoding portion 322 performs theprocessing in the 0th to (M_(c)−M)th steps, and finally demodulates allelements of x_(Bi) from the symbol z′=[z′₁ to z′_(Mc)]^(T), acquires thesymbol x″=[x″₁ to x″_(Mc)]^(T), and outputs them to the second decodingportion 324.

Notably, the amount of computing required by the first decoding portion322 for performing the maximum likelihood decoding in the 0th to the(M_(c)−M)th steps by using groups of M elements of the symbolx_(Bi)=[x_(i,1) to x_(i,Mc)]^(T) is remarkable less than the amount ofcomputing for performing maximum likelihood decoding on all of theelements of the symbol x_(Bi)=[x_(i,1) to x_(i,Mc)]^(T) at one time.

When the values of M_(p) bits are 1 and the values of the other bits are0 among M_(c) bits of the symbol x″=[x″₁ to x″_(Mc)]^(T), the bit countof the value 1 in the symbol x=[x₁ to x_(Mc)]^(T) created by the PCmapping portion 204 in the transmission program 30 agrees with the bitcount of the value 0. Therefore, there is a high possibility that thesymbol x″=[x″₁ to x″_(Mc)]^(T) are equal to x=[x₁ to x_(Mc)]^(T) createdfrom M_(pc)-bit message data input from the transmission program 30.

On the other hand, except for the time when the values of M_(p) bits are1 and the values of the other bits are 0 among M_(c) bits in the symbolx″=[x″₁ to x″_(Mc)]^(T), the bit count of the value 1 in the symbolx=[x₁ to x_(Mc)]^(T) created by the PC mapping portion 204 in thetransmission program 30 agrees with the bit count of the value 0.Therefore, there are no possibilities that the symbol x″=[x″₁ tox″_(Mc)]^(T) are equal to X=[x₁ to x_(Mc)]^(T) created from M_(pc)-bitmessage data input from the transmission program 30.

[Case where the Decoding Result by First Decoding Portion is Determinedas Right by Second Decoding Portion]

The second decoding portion 324 determines, in accordance with the factdescribed above, whether the values of M_(p) bits are 1 and the valuesof the other bits are 0 among M_(c) bits in the symbol x″=[x″₁ tox″_(Mc)]^(T) input from the first decoding portion 322 or not, decodesthe symbol x′=[x′₁ to x′_(Mc)]^(T) being the final decoding result andoutputs them to the PC demapping portion 326.

In other words, when the values of M_(p) bits are 1 and the values ofthe other bits are 0 among the M_(c) bits in the symbol x″=[x″₁ tox″_(Mc)]^(T), the second decoding portion 324 outputs the symbol x″=[x″₁to x″_(Mc)]^(T) input from the first decoding portion 322 to the PCdemapping portion 326 as the symbol x′=[x′₁ to x′_(Mc)]^(T) being thefinal decoding result.

FIG. 10 is a histogram illustrating the results of acquisition of thefrequencies of appearance by a computer simulation of the bit count ofthe value 1 included in the symbol x″=[x″₁ to x″_(Mc)]^(T) in thedecoding result by the first decoding portion 322 shown in FIG. 7.

However, FIG. 10 shows the case where M_(c)=16, M_(p)=8, ΔfT=0.75,E_(b)/N₀=6 bB, and M=7.

FIG. 10 shows that there is a significantly high probability that thedecoding result can be acquired by the first decoding portion 322, whichhas a high possibility that the symbol x″=[x″₁ to x″_(Mc)]^(T) by thefirst decoding portion 322 includes M_(p) bits with the value 1 and areequal to the symbol x=[x₁ to x_(Mc)]^(T) created by th PC mappingportion 204 in the transmission program 30 (in FIG. 6).

Therefore, in this case, the frequency requiring the maximum likelihooddecoding in the second decoding portion 324 is significant low, andmostly, a less amount of computing by the first decoding portion 322 isrequired to decode the symbol x′=[x′₁ to x′_(Mc)]^(T).

When, among M_(c) bits of the symbol x″=[x″₁ to x″_(Mc)]^(T), the valuesof M_(p) bits are 1 and the values of the other bits are 0, the seconddecoding portion 324 acquires the symbol x″=[x″₁ to x″_(Mc)]^(T) fromthe first decoding portion 322, handles them directly as the symbolx′=[x′₁ to x′_(Mc)]^(T) and outputs the result to the PC demappingportion 326.

[Case where Second Decoding Portion Determines that the Decoding Resultby First Decoding Portion is Wrong]

On the other hand, when the bit count of the value 1 actually includedin the symbol x″=[x″₁ to x″_(Mc)]^(T) decoded by the first decodingportion 322 is M′_(p) and M_(p)<M′_(p), unnecessary bits of the value 1of N₁=M′_(p)−M_(p) are included.

Therefore, by replacing the value 1 of N₁ bits by the value 0, thesymbol x″=[x″₁ to x″_(Mc)]^(T) acquired by the first decoding portion322 can be brought closer to x=[x₁ to x_(Mc)]^(T).

However, when N₁ is high, the number of replacement methods from thevalue-1 bits to the value-0 bits in x″=[x″₁ to x″_(Mc)]^(T) increases.Therefore, practically, the upper limit of the bit count for thereplacement is preferably limited by the replacement depth d (whered≦N₁).

Notably, when d=N₁, all possible replacements are to be performed.

The newly created vector (set) as a result of the replacement in thisway is x_(B) ^((v)), and the symbol x′=[x′₁ to x′_(Mc)]^(T) can beacquired by Expression 21 below.

$\begin{matrix}{x^{\prime} = {\arg {\min\limits_{v}( {{{Q^{H}y} - {Rx}_{\mathcal{B}}^{\prime {(v)}}}} )}}} & \lbrack {{Expression}\mspace{14mu} 21} \rbrack\end{matrix}$

In such a case, the number of x_(B) ^((v))s to be compared with thesymbol z′=[z′₁ to z′_(Mc)]^(T) is (M′_(p)/d). Thus, even when thedecoding by the second decision portion 324 is added to the decodingprocessing only by the first decoding portion 322, the amount ofcomputing does not largely increase.

Notably, when M_(p)>M′_(p), N₂=M_(p)−M′_(p) value-1 bits are lacking.

Therefore, by replacing N₂ value-0 bits by the value 1, the symbolx″=[x″₁ to x″_(Mc)]^(T) acquired by the first decoding portion 322 canbe brought closer to x=[x₁ to x_(Mc)]^(T).

Also in this case, it is effective to limit the bit count for thereplacement by the replacement depth d (d≦N₂), and the number of x_(B)^((v))s to be compared with the symbol z′=[z′₁ to z′_(Mc)]^(T) is(M_(c)−M′_(p)/d). Therefore, even when the decoding by the seconddecision portion 324 is added to the decoding processing only by thefirst decoding portion 322, the amount of computing is not largelyincreased.

Therefore, even when the decoding is performed by the second decodingportion 324, the increment from the amount of computing by the firstdecoding portion 322 is small.

The PC demapping portion 326 performs the processing corresponding tothe PC mapping portion 204 in the transmission program 30 (in FIG. 6),creates the M_(pc)-bit message data corresponding to x′=[x′₁ tox′_(Mc)]^(T) acquired as the result of the decoding, and outputs it tothe P/S 212 in a parallel form.

The P/S 212 transforms the message data input from the PC demappingportion 326 to the one in a serial form and externally outputs theresult through the data output IF 126.

[Overall Operations by Communication System 1]

Taking the case where the communication apparatus 2-1 is the source (Tx)and the communication apparatus 2-2 is the receiver side (Rx) as anexample, the overall operations by the communication system 1 (in FIG.3) will be described below.

[Transmission Operation]

The PC mapping portion 204 of the transmission program 30 (FIG. 6) thatoperates in the communication apparatus 2-1 maps the M_(pc)-bit messagedata externally input through the data input IF 120 and transformed tothe one in a parallel form by the S/P 202 to M_(t) bit symbol x_(B)=[x₁to x_(Mt)]^(T).

The matrix computing portion 300 multiplies the symbol x_(B)=[x₁ tox_(c)]^(T) input from the PC mapping portion 204 by the matrix Fexpressed in Expression 10 to perform the first transformation, acquiresthe sample y=[y₁ to y_(Mt)]^(T), and outputs the elements to themultiplexing portions 210-1 to 210-M_(t).

The multiplexing portions 210-1 to 210-M_(t) multiply the coefficientsw₁ to w_(Mt) created by the coefficient setting portion 208 by theelements of the sample y=[y₁ to y_(Mt)]^(T).

Notably, the sample y=[y₁ to y_(Mt)]^(T) acquired as the multiplicationresult by the multiplexing portion 210-1 to 210-M_(t) may be transformedto a table form by using the matrix W expressed in Expression 12.

As described above, the matrices F and W expressed in Expression 10 andExpression 11 have a relationship of WF=QR between the complex conjugatetransposition matrix Q (in Expression 13) of the matrix Q^(H) to be usedfor transformation to the sample y′=[y′₁ to y′_(Mt)]^(T) of the symbolz′=[z′₁ to z′_(Mc)]^(T) in the reception program 32 (in FIG. 8) and thematrix R (in Expression 14).

Like the description on the transmission program 30, the matrices Q andR are used in the case where the coefficient setting portion 208 andmultiplexing portion 210 are omitted, for clear description below.

The sample y=[y₁ to y_(Mt)]^(T) are transformed to the transmit signaly(t) at the baseband by the P/S 212 and D/A 214 and are transformed tothe transmit signal compatible with the communication line to be used bythe transmitting portion 130 (in FIG. 5) and are transmitted to thedestination communication apparatus 2-2 through the communication line.

[Reception Operation]

As described above, an unnecessary signal component n(t) is superimposedon transmit signal on a communication line, and the transmit signal arereceived by the communication apparatus 2-2 as the transmit signaly′(t)=y(t)+n(t).

The A/D 220 and S/P 202 of the reception program 32 (in FIG. 8)operating in the communication apparatus 2-2 transform the transmitsignal y′ (t)=y(t)+n(t) to the sample y′=WFx_(B)+η=[y′₁ to y′_(Mt)]^(T)in a parallel form and output them to the matrix computing portion 320.

The matrix computing portion 320 multiplies the sample y′ by the matrixQ^(H) to perform the second transformation and outputs the samplez′=[z′₁ to z′_(Mc)]^(T) acquired as the result of the secondtransformation to the first decoding portion 322.

As described with reference to Expression 16 to Expression 18, the firstdecision portion 322 repeats the processing of using a group of Melements of the sample z′=[z′₁ to z′_(Mc)]^(T) to decode the M_(c)th to(M_(c)−M−1)th bits on a bit-by-bit basis M_(c) to M_(c)−M−1 times.

As described with reference to Expression 20, the first decision portion322 in the final (n=M_(c)−M)th decoding processing collectively decodesthe values of the first to Mth bits of the symbol x_(Bi)=[x_(i,1) tox_(i,Mc)]^(T).

The first decision portion 322 performs the decoding processing todecode all bits of the symbol x″=[x″₁ to x″_(Mc)]^(T) finally.

When the values of M_(p) bits are 1 and the value of the other bits are0 among the M_(c) bits of the symbol x″=[x″₁ to x″_(Mc)]^(T) input fromthe first decoding portion 322, the second decoding portion 324transforms the symbol x″=[x″₁ to x″_(Mc)]^(T) input from the firstdecoding portion 322 to the symbol x′=[x′₁ to x′_(Mc)]^(T), which is thefinal decoding result.

In other cases, the second decoding portion 324, as described withreference to Expression 21, performs the maximum likelihood decoding onthe entire sample z′=[z′₁ to z′_(Mc)]^(T) and acquires the symbolx′=[x′₁ to x′_(Mc)]^(T) as the result.

The second decoding portion 324 outputs the symbol x′=[x′₁ tox′_(Mc)]^(T) acquired by the decoding processing to the PC demappingportion 326.

The PC demapping portion 326 creates the M_(pc)-bit message datacorresponding to the sample x′=[x′₁ to x′_(Mc)]^(T) acquired as theresult of the decoding and outputs it to the P/S 212 in a parallel form.

The P/S 212 transforms the message data input from the PC demappingportion 326 to the one in a serial form and externally outputs theresult through the data output IF 126 (in FIG. 5).

[Characteristics of CR-PC/HC-MCM]

The characteristics of CR-PC/HC-MCM will be described below.

FIG. 11 is a graph showing a relationship between BER values occurringin the symbol x′ decoded by the reception program 32 shown in FIG. 7 andthe values of E_(b)/N₀.

Notably, FIG. 11 shows the case where M_(c)=16, M_(p)=8, ΔfT=0.75, andM=7.

As shown in FIG. 11, the BER values of the symbol x=[x₁ to x_(Mc)]^(T)decoded by the reception program 32 from the transmit signal on which anunnecessary signal component is superimposed and the message data to bedecoded subsequently become worse to some extent, compared with the casewhere no unnecessary signal components are superimposed on transmitsignal and the destination communication apparatus 2-2 the transmitsignal completely to the symbol x=[x₁ to x_(Mc)]^(T) by maximumlikelihood decoding.

However, the BER values of the symbol x′=[x′₁ to x′_(Mc)]^(T) decoded bythe reception program 32 and the message data to be decoded subsequentlyare improved as the depth d increases from d=0 (corresponding to thecase where maximum likelihood decoding is not performed by the seconddecoding portion 324) sequentially to d=1 to 3 (corresponding to thecase where the second decoding portion 324 performs maximum likelihooddecoding within the range that the value of |N₁| are 1 to 3 and approachthe BER value in the case where maximum likelihood decoding is performedin the communication apparatus 2-2.

FIG. 12 shows a table showing the highest amounts of computing for themaximum likelihood decoding by the communication apparatus 2 shown inFIG. 2 and decoding by the first decoding portion 322 and seconddecoding portion 324 of the reception program 32 shown in FIG. 7.

FIG. 12 also shows the case where M_(c)=16, M_(p)=8 and M=7.

Both in the receiver 22 and the reception program 32, the highest amountof computing is required for calculating the Euclid distance between thesymbol z′ and a replica symbol.

As shown in FIG. 12, the amount of computing by the reception program 32in the case where the depths d=0 to 3 are as significantly low as1/6.40, 1/6.36, 1/6.18 and 1/5.67, and the increase in amount ofcomputing according to the increase in depth d is less.

The embodiment has been provided for illustration and descriptionpurposes only and does not cover all of the embodiments of the claimedinvention.

It is not intended that the embodiment limits the technological range ofthe claimed invention to the disclosed details. The embodiment may bechanged and altered in various manners on the basis of the discloseddetails.

The embodiment has been selected and been described such that theprinciple and actual applications of the claimed invention can bedescribed best. Therefore, a person skilled in the art can use theclaimed invention and the embodiments by making various changes thereonfor optimizing all possible actual applications on the basis of thedisclosed details of the embodiment.

It is intended that the technological range of the claimed invention isdetermined on the basis of the descriptions or equivalents thereof.

The communication system, data decoding apparatus and data receivingmethod data according to the present invention are applicable forcommunication.

1. A communication system comprising: a transmitting apparatus; and areceiving apparatus, the transmitting apparatus having: a mapper formapping each value of all transmission objective data to each of firstsymbols including a first number of data in which each of thetransmission objective data including a predetermined bits, and beingobjective of transmission by combinations a second number of carrierwaves being less than the first number of carrier waves being usable fortransmission, the sorts of values of the transmission objective databeing same or less than the sorts of values being represented by thepredetermined number of bits, and each of the first symbols representingeach value of the transmission objective data by setting which of thesecond number of data to a predetermined first value and setting therest of the second data to a second value being other than the firstvalue; a first transformer for performing a first transformation totransform the first symbol into transmission signal that including firstsample having third number of data by having the first symbol be a firstnumber×1 first vector to multiple the first vector by a firstnumber×third number (third number>first number) matrix, in which theresult of first multiplication of the first matrix by the firstnumber×the first number diagonal matrix that corresponding to themultiplication of each of a third number of data included in the firstsample obtained by the first transformation by each of secondcoefficients for third number of data included in the first sample beingequal to the result of second multiplication of an a third number×firstnumber upper triangular matrix by a third number×third numbernon-singular matrix in a complex form, and the non-singular matrix, andthe upper triangular matrix being given such that the result of thefirst multiplication and the result of the second multiplication beingequal in accordance with the first matrix and the diagonal matrix;multiplier for multiplying each of the first samples included in thetransmission signal by each of the second coefficients; and atransmitter for transmitting the transmission signal including the thirdnumber of signals to the receiving apparatus, the receiving apparatushaving: a receiver for receiving the transmission signal havingpossibility to include a different signal component from thetransmission signal from the transmitting apparatus; a secondtransformer for performing a second transformation to transform thecomplex conjugate inverse matrix in the non-singular matrix into thesecond sample corresponding to the multiplication result of the uppertriangular matrix by the first vector by having the third number of dataincluded in the first sample included in the received transmissionsignal be a second vector of the third number×1 format to multiply thecomplex conjugate inverse matrix in the non-singular matrix by thesecond vector; a first decoder for sequentially performing firstdecoding on the data included in the third number of second sampleacquired by the second transformation and acquiring groups eachincluding the fourth number of data (the first number within the firstsymbol>fourth number to sequentially decode parts of the second symbolcorresponding to the first symbol for acquiring the entire secondsymbol; a second decoder, if the second symbol decoded by the firstdecoding would include the second number of the first values, for havingthe second symbol acquired by the first decoding be the first symbol, orif not, for performing second decoding on all of the third number ofsecond sample to have the symbol acquired by the second decoding be thesecond symbol; and a demapper that decodes the transmission objectivedata from the first symbol acquired by the second decoder, wherein: thefirst decoding is implemented by performing maximum likelihood decodingon the third number of second sample with all of the results of themultiplication of the fourth number (the first number>fourth number) ofelements within the first symbol by the fourth number×1 upper triangularmatrix of the vector; the second decoding is implemented by selecting acombination having the nearest value to the third number of secondsample value among the combinations of the second sample correspondingto the second symbol acquired by the first decoding of which the firstvalues being different from the second number; and the second decodingis implemented by selecting a combination having the nearest value tothe second sample corresponding to the second symbol acquired by thefirst decoding to have the first value data of which number beingdifferent from the second value among the first sample corresponding tothe second symbol including an equal number of the first value data tothe first symbol, the first sample being acquired by replacing value ofthe first value data to the second value in the second symbol acquiredby the first decoding to have the first value data of which number beingdifferent from the second number to the second value within apredetermined range.
 2. A data decoding apparatus for receivingtransmission signal to decode transmission objective data from thereceived transmission signal, in which the transmission signal beinggenerated by mapping each value of all transmission objective data toeach of first symbols including a first number of data, each of thetransmission objective data including a predetermined bits and beingobjective of transmission by combinations a second number of carrierwaves being less than the first number of carrier waves being usable fortransmission, the sorts of values of the transmission objective databeing same or less than the sorts of values being represented by thepredetermined number of bits, transforming the first symbol to thetransmit signal including the first sample having a third number (thirdnumber>first number) of data to decode the transmission target data fromthe received transmit signal, and each of the first symbols representingeach value of the transmission objective data by setting which of thesecond number of data to a predetermined first value and setting therest of the second data to a second value being other than the firstvalue, a receiver for receiving the transmission signal havingpossibility to include a different signal component from thetransmission signal; a transformer for transforming the receivedtransmission signal to a second sample having the third number of datacorresponding to the first sample; a first decoder for sequentiallyperforming first decoding on a third number of data included in theacquired second sample to decode second symbol corresponding to thefirst symbol by sequentially decoding parts of the second symbolcorresponding to the first symbol; a second decoder, if the secondsymbol acquired by the first decoding would include second number of thefirst value data, for having the second symbol acquired by the firstdecoding be the first symbol, or if not, for performing second decodingon all of the data held by the second sample to have the second symbolacquired by the second decoding be the first symbol; and a demapper thatdecodes the transmission target data from the first symbol acquired bythe second decoder.
 3. The data decoding apparatus according to claim 2,wherein: the first value is bit value 1; the second value is bit value0; the third number of data included in the first symbol and the firstnumber of data included in the second symbol are the first number ofbits; the second decoder determines that there is a possibility that thesecond symbol decoded by the first decoding is identical to the firstsymbol corresponding to the second symbol if the number of value-1 bitsincluded in the second symbol decoded by the first decoding is equal tothe second number and determines that there is no possibilities that thesecond symbol decoded by the first decoding is identical to the firstsymbol corresponding to the second symbol if not.
 4. The data decodingapparatus according to claim 2, wherein the first decoder performs thefirst decoding by sequentially selecting a combination having thehighest possibility of being identical to the fourth number of dataincluded in the second sample.
 5. The data decoding apparatus accordingto claim 4, wherein the fourth number of all possible combinations ofdata included in the second sample is acquired by transforming the allpossible fourth number of data included in the first symbol to the firstsample and performing the transformation by the transformer on thetransformed first sample.
 6. The data decoding apparatus according toclaim 4, wherein the first decoder sequentially performs the firstdecoding on the fourth number of data excluding the data, which hasalready been handled as the target of the first decoding, to finallyacquire the entire second symbol.
 7. The data decoding apparatusaccording to claim 4, wherein the second decoder performs the seconddecoding by selecting one having the highest possibility of beingidentical to the second sample acquired by performing the transformationby the transformer on the second symbol, which is acquired by the firstdecoding, having no possibilities of being identical to the first symbolamong the combinations of the second sample corresponding to the entiresecond symbol, which are acquired as the result of a predeterminedoperation on the second symbol if there is no possibilities that thesecond symbol acquired by the first decoding is identical to the firstsymbol.
 8. The data decoding apparatus according to claim 7, wherein:the third number of data included in the first symbol and the thirdnumber of data included in the second symbol are the third number ofbits; and the second sample to be selected is all combinations of thesecond sample corresponding to all of the second symbol acquired bychanging the second symbol having no possibilities of being identical tothe first symbol such that the difference between the number of value-1bits included in the second symbol and the number of value-1 bitsincluded in the first symbol can be within a predetermined range.
 9. Thedata decoding apparatus according to claim 2, wherein: thetransformation of the first symbol to a transmission signal includingthe third number of first sample, which are more than the first numberof the first symbol, is performed by transforming the first symbol to atransmission signal including the first sample held by the third numberof data by handling the first symbol as a first number×1 first vectorand multiplying the first vector by a first number×third number firstmatrix (where the third number is higher than the first number); theresult of first multiplication of the first matrix by the firstnumber×first number diagonal matrix, which corresponds to themultiplication between the third number of data held by the firstsample, which are acquired by the transformation and second coefficientsfor the third number of data is equal to the result of secondmultiplication of a third number×third number non-singular matrix in acomplex form by an a third number×first number upper triangular matrix,and the non-singular matrix and the upper triangular matrix are givensuch that the first multiplication result and the second multiplicationresult can be equal in accordance with the first matrix and the diagonalmatrix, and the transformer multiplies the inverse matrix of thenon-singular matrix by the third number of data of the first sampleincluded in the received transmission signal as a third number×1 secondvector to transform to the second sample corresponding to the result ofthe multiplication of the second vector by the upper triangular matrixthereby.
 10. A data decoding method for receiving transmission signal todecode transmission objective data from the received transmissionsignal, in which the transmission signal being generated by mapping eachvalue of all transmission objective data to each of first symbolsincluding a first number of data, each of the transmission objectivedata including a predetermined bits and being objective of transmissionby combinations a second number of carrier waves being less than thefirst number of carrier waves being usable for transmission, the sortsof values of the transmission objective data being same or less than thesorts of values being represented by the predetermined number of bits,transforming the first symbol to the transmit signal including the firstsample having a third number (third number>first number) of data todecode the transmission target data from the received transmit signal,and the first symbols representing each value of the transmissionobjective data by setting which of the second number of data to apredetermined first value and setting the rest of the second data to asecond value being other than the first value, the method comprising thesteps of: receiving the transmission signal having possibility toinclude a different signal component from the transmission signal;transforming the received transmission signal to a second sample havingthe third number of data corresponding to the first sample; sequentiallyperforming first decoding on a third number of data included in theacquired second sample to decode second symbol corresponding to thefirst symbol by sequentially decoding parts of the second symbolcorresponding to the first symbol; if the second symbol acquired by thefirst decoding would include second number of the first value data,having the second symbol acquired by the first decoding be the firstsymbol, or if not, for performing second decoding on all of the dataheld by the second sample to have the second symbol acquired by thesecond decoding be the first symbol; and decoding the transmissionobjective data from the first symbol acquired by the second decoding.11. The data decoding method according to claim 10, wherein: the firstvalue is bit value 1; the second value is bit value 0; the third numberof data included in the first symbol and the first number of dataincluded in the second symbol are the first number of bits; the seconddecoding includes determining that there is a possibility that thesecond symbol decoded by the first decoding is identical to the firstsymbol corresponding to the second symbol if the number of value-1 bitsincluded in the second symbol decoded by the first decoding is equal tothe second number and determining that there is no possibilities thatthe second symbol decoded by the first decoding is identical to thefirst symbol corresponding to the second symbol if not.
 12. The datadecoding method according to claim 13, wherein the first decodingincludes performing the first decoding by sequentially selecting acombination having the highest possibility of being identical to thefourth number of data included in the second sample.
 13. The datadecoding method according to claim 12, wherein the fourth number of allpossible combinations of data included in the second sample is acquiredby transforming the all possible fourth number of data included in thefirst symbol to the first sample and performing the transformation forthe received transmission signal on the transformed first sample. 14.The data decoding method according to claim 13, wherein the firstdecoding includes sequentially performing the first decoding on thefourth number of data excluding the data, which has already been handledas the target of the first decoding, to finally acquire the entiresecond symbol.
 15. The data decoding method according to claim 13,wherein the second decoding includes performing the second decoding byselecting one having the highest possibility of being identical to thesecond sample acquired by performing the transformation by thetransformer on the second symbol, which is acquired by the firstdecoding, having no possibilities of being identical to the first symbolamong the combinations of the second sample corresponding to the entiresecond symbol, which are acquired as the result of a predeterminedoperation on the second symbol if there is no possibilities that thesecond symbol acquired by the first decoding is identical to the firstsymbol.
 16. The data decoding method according to claim 15, wherein: thethird number of data included in the first symbol and the third numberof data included in the second symbol are the third number of bits; andthe second sample to be selected is all combinations of the secondsample corresponding to all of the second symbol acquired by changingthe second symbol having no possibilities of being identical to thefirst symbol such that the difference between the number of value-1 bitsincluded in the second symbol and the number of value-1 bits included inthe first symbol can be within a predetermined range.
 17. The datadecoding method according to claim 10, wherein: the transformation ofthe first symbol to a transmission signal including the third number offirst sample, which are more than the first number of the first symbol,is performed by transforming the first symbol to a transmission signalincluding the first sample held by the third number of data by handlingthe first symbol as a first number×1 first vector and multiplying thefirst vector by a first number×third number first matrix (where thethird number is higher than the first number); the result of firstmultiplication of the first matrix by the first number×first numberdiagonal matrix, which corresponds to the multiplication between thethird number of data held by the first sample, which are acquired by thetransformation and second coefficients for the third number of data isequal to the result of second multiplication of a third number×thirdnumber non-singular matrix in a complex form by a third number×firstnumber upper triangular matrix, and the non-singular matrix and theupper triangular matrix are given such that the first multiplicationresult and the second multiplication result can be equal in accordancewith the first matrix and the diagonal matrix, and the first decodingincludes multiplying the inverse matrix of the non-singular matrix bythe third number of data of the first sample included in the receivedtransmission signal as a third number×1 second vector to transform tothe second sample corresponding to the result of the multiplication ofthe second vector by the upper triangular matrix thereby.